






a						:			Union[str, Any]     	=					[
    "Audio",
    "Array2D",
    "Array3D",
    "Array4D",
    "Array5D",
    "ClassLabel",
    "Features",
    "Sequence",
    "Value",
    "Image",
    "Translation",
    "TranslationVariableLanguages",
]
from .audio import Audio
from .features import ArrayaD, ArrayaD, ArrayaD, ArrayaD, ClassLabel, Features, Sequence, Value
from .image import Image
from .translation import Translation, TranslationVariableLanguages



"""simple docstring"""


from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   List[Any]:




						'''simple docstring'''



						def is_in_circle(__lowerCAmelCase  ,       __lowerCAmelCase							) -> bool:
												lowerCamelCase__   =sqrt((x**2) + (y**2)							)
												# Our circle has a radius of 1, so a distance
												# greater than 1 would land outside the circle.
												return distance_from_centre <= 1

						# The proportion of guesses that landed in the circle
						lowerCamelCase__   =mean(
						    int(is_in_circle(uniform(-1.0  ,       1.0							)  ,       uniform(-1.0  ,       1.0							)							)							)
						    for _ in range(__lowerCAmelCase							)							)
						# The ratio of the area for circle to square is pi/4.
						lowerCamelCase__   =proportion * 4
						print(F'''The estimated value of pi is {pi_estimate}'''							)
						print(F'''The numpy value of pi is {pi}'''							)
						print(F'''The total error is {abs(pi - pi_estimate							)}'''							)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase = 0.0  ,       __lowerCAmelCase = 1.0  ,       )				->   float:




						'''simple docstring'''



						return mean(
						    function_to_integrate(uniform(__lowerCAmelCase  ,       __lowerCAmelCase							)							) for _ in range(__lowerCAmelCase							)							) * (max_value - min_value)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase = 0.0  ,       __lowerCAmelCase = 1.0							)				->   None:




						'''simple docstring'''



						def identity_function(__lowerCAmelCase							) -> float:
												return x

						lowerCamelCase__   =area_under_curve_estimator(
						    __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)
						lowerCamelCase__   =(max_value * max_value - min_value * min_value) / 2

						print("******************"							)
						print(F'''Estimating area under y=x where x varies from {min_value} to {max_value}'''							)
						print(F'''Estimated value is {estimated_value}'''							)
						print(F'''Expected value is {expected_value}'''							)
						print(F'''Total error is {abs(estimated_value - expected_value							)}'''							)
						print("******************"							)





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   None:




						'''simple docstring'''



						def function_to_integrate(__lowerCAmelCase							) -> float:
												return sqrt(4.0 - x * x							)

						lowerCamelCase__   =area_under_curve_estimator(
						    __lowerCAmelCase  ,       __lowerCAmelCase  ,       0.0  ,       2.0							)

						print("******************"							)
						print("Estimating pi using area_under_curve_estimator"							)
						print(F'''Estimated value is {estimated_value}'''							)
						print(F'''Expected value is {pi}'''							)
						print(F'''Total error is {abs(estimated_value - pi							)}'''							)
						print("******************"							)


if __name__ == "__main__":
	import doctest

	doctest.testmod()


